300 research outputs found

    Metastable legged-robot locomotion

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-215).A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.by Katie Byl.Ph.D

    Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem

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    Given a submersion π:Q→M\pi:Q \to M with an Ehresmann connection H\mathcal{H}, we describe how to solve Hamiltonian systems on MM by lifting our problem to QQ. Furthermore, we show that all solutions of these lifted Hamiltonian systems can be described using the original Hamiltonian vector field on MM along with a generalization of the magnetic force. This generalized force is described using the curvature of H\mathcal{H} along with a new form of parallel transport of covectors vanishing on H\mathcal{H}. Using the Pontryagin maximum principle, we apply this theory to optimal control problems MM and QQ to get results on normal and abnormal extremals. We give a demonstration of our theory by considering the optimal control problem of one Riemannian manifold rolling on another without twisting or slipping along curves of minimal length.Comment: 31 page

    Topology based representations for motion synthesis and planning

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    Robot motion can be described in several alternative representations, including joint configuration or end-effector spaces. These representations are often used for manipulation or navigation tasks but they are not suitable for tasks that involve close interaction with the environment. In these scenarios, collisions and relative poses of the robot and its surroundings create a complex planning space. To deal with this complexity, we exploit several representations that capture the state of the interaction, rather than the state of the robot. Borrowing notions of topology invariances and homotopy classes, we design task spaces based on winding numbers and writhe for synthesizing winding motion, and electro-static fields for planning reaching and grasping motion. Our experiments show that these representations capture the motion, preserving its qualitative properties, while generalising over finer geometrical detail. Based on the same motivation, we utilise a scale and rotation invariant representation for locally preserving distances, called interaction mesh. The interaction mesh allows for transferring motion between robots of different scales (motion re-targeting), between humans and robots (teleoperation) and between different environments (motion adaptation). To estimate the state of the environment we employ real-time sensing techniques utilizing dense stereo tracking, magnetic tracking sensors and inertia measurements units. We combine and exploit these representations for synthesis and generalization of motion in dynamic environments. The benefit of this method is on problems where direct planning in joint space is extremely hard whereas local optimal control exploiting topology and metric of these novel representations can efficiently compute optimal trajectories. We formulate this approach in the framework of optimal control as an approximate inference problem. This allows for consistent combination of multiple task spaces (e.g. end-effector, joint space and the abstract task spaces we investigate in this thesis). Motion generalization to novel situations and kinematics is similarly performed by projecting motion from abstract representations to joint configuration space. This technique, based on operational space control, allows us to adapt the motion in real time. This process of real-time re-mapping generates robust motion, thus reducing the amount of re-planning.We have implemented our approach as a part of an open source project called the Extensible Optimisation library (EXOTica). This software allows for defining motion synthesis problems by combining task representations and presenting this problem to various motion planners using a common interface. Using EXOTica, we perform comparisons between different representations and different planners to validate that these representations truly improve the motion planning
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